Question: Simplify the following expression: $k = \dfrac{6ac + 3c^2}{c^2 - 2bc} + \dfrac{2bc + c^2}{c^2 - 2bc}$ You can assume $a,b,c \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{6ac + 3c^2 + 2bc + c^2}{c^2 - 2bc}$ $k = \dfrac{6ac + 4c^2 + 2bc}{c^2 - 2bc}$ The numerator and denominator have a common factor of $c$, so we can simplify $k = \dfrac{6a + 4c + 2b}{c - 2b}$